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arXiv · 1204.4571

A second derivative Hölder estimate for weak mean curvature flow

Yoshihiro Tonegawa
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Abstract

We give a proof that Brakke's mean curvature flow under the unit density assumption is smooth almost everywhere in space-time. More generally, if the velocity is equal in a weak sense to its mean curvature plus some given α-Hölder continuous vector field, then we show C^{2,α} regularity almost everywhere.

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Yoshihiro Tonegawa. 2012-04-20. A second derivative Hölder estimate for weak mean curvature flow. https://doi.org/10.1515/acv-2013-0104

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